In triangle ABC, AD : DB = 2 : 3, DE is parallel to BC.
Assertion (A) : $\dfrac{\text{DE}}{\text{BC}} = \dfrac{\text{AD}}{\text{BD}} = \dfrac{2}{3}$ .
Reason (R) : $\dfrac{\text{DE}}{\text{BC}} = \dfrac{\text{AD}}{\text{AB}} = \dfrac{2}{5}$ .
A is true, R is false.
A is false, R is true.
Both A and R are true and R is correct reason for A.
Both A and R are true and R is incorrect reason for A.

Question

In triangle ABC, AD : DB = 2 : 3, DE is parallel to BC.

Assertion (A) : $\dfrac{\text{DE}}{\text{BC}} = \dfrac{\text{AD}}{\text{BD}} = \dfrac{2}{3}$ .

Reason (R) : $\dfrac{\text{DE}}{\text{BC}} = \dfrac{\text{AD}}{\text{AB}} = \dfrac{2}{5}$ .

A is true, R is false.
A is false, R is true.
Both A and R are true and R is correct reason for A.
Both A and R are true and R is incorrect reason for A.

KnowledgeBoat · Accepted Answer

In Δ ADE and Δ ABC ⇒ ∠DAE = ∠BAC (Common angle) ⇒ ∠ADE = ∠ABC (Corresponding angles are equal) ⇒ ∠AED = ∠ACB (Corresponding angles are equal) ∴ Δ ADE ∼ Δ ABC (By AAA postulate) According to basic proportionality theorem, if a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, then the other two sides are divided in the same ratio. So, assertion is true but reason is false. Hence, option 1 is the correct option.

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